Numerical evaluator of integrals implementing the "Sector Decomposition" method (see arXiv:1703.09692, arXiv:hepph/0004013, arXiv:0803.4177).
Project description
pySecDec
pySecDec is a toolbox for the calculation of dimensionally regulated parameter integrals using the sector decomposition approach.
See 2108.10807, 1811.11720, and 1703.09692 for description of the implementation; 0803.4177 and hepph/0004013 for description of sector decomposition; and 1502.06595 for SecDec, the predecessor of pySecDec.
Installation
pySecDec should work under Python version 3.6 or newer on the usual Unixlike systems.
The latest release can be installed from PyPI by first upgrading pip:
$ python3 m pip install user 'pip>=20.1'
and then running:
$ python3 m pip install user upgrade pySecDec
The geometric method and Normaliz
If you want to use the geometric decomposition methods
(decomposition_method='geometric'
or 'geometric_ku'
),
you need the normaliz
executable,
which can be downloaded from https://www.normaliz.uniosnabrueck.de
[W. Bruns and B. Ichim and T. Römer and R. Sieg and C. Söger].
The geometric decomposition module is
designed for normaliz version 3  currently versions
3.3.0
, 3.4.0
, 3.5.4
, 3.6.0
, 3.6.2
, 3.7.3
,
3.7.4
, and 3.8.1
are known to work. We recommend to set your $PATH such that the
normaliz
executable is found. Alternatively, you can pass the path to the normaliz
executable directly to the functions that need it.
Additional dependencies for generated C++ packages
The intended main usage of pySecDec is to make it write C++ packages using the functions
pySecDec.code_writer.make_package
and pySecDec.loop_integral.loop_package
.
In order to build these C++ packages, the following additional nonpythonbased libraries
and programs are required:

CUBA (http://www.feynarts.de/cuba/)

FORM (http://www.nikhef.nl/~form/)

SecDecUtil (part of pySecDec), and its dependency:
The functions pySecDec.code_writer.make_package
and
pySecDec.loop_integral.loop_package
can use the external program
dreadnaut
to find all sector symmetries and therefore reduce
the number of sectors:
 NAUTY (http://pallini.di.uniroma1.it/) [B. D. McKay and A. Piperno, Practical graph isomorphism, II, 2014, Journal of Symbolic Computation, 60, 94112, doi:10.1016/j.jsc.2013.09.003]
These packages are redistributed along with pySecDec itself, and will be built automatically during pySecDec installation.
Basic Usage
You can find the pySecDec manual over at https://secdec.readthedocs.io.
Additionally, the development repository contains a folder examples
with examples of pySecDec usage.
A simple example of the evaluation of a loop integral with pySecDec is box1L
.
This example computes a oneloop box with one offshell leg (with offshellness s1) and one internal massive line (with mass squared msq).
To run this example change into the box1L
directory and run the commands:
$ python3 generate_box1L.py
$ make C box1L
$ python3 integrate_box1L.py
The file generate_box1L.py
defines the loop integral and calls pySecDec to perform the sector decomposition.
Once run it produces the directory box1L
which contains the code required to numerically evaluate the integral.
The make
command builds this code and produces a library.
The file integrate_box1L.py
loads the integral library and evaluates the integral for a specified numerical point.
This will print the result of the integral evaluated with Mandelstam invariants s=4.0, t=0.75 and s1=1.25, msq=1.0:
eps^2: 0.142868356275422825  1.63596224151119965e6*I +/ ( 0.00118022544307414272 + 0.000210769456586696187*I )
eps^1: 0.639405625715768089 + 1.34277036689902802e6*I +/ ( 0.00650722394065588166 + 0.000971496627153705891*I )
eps^0 : 0.425514350373418893 + 1.86892487760861536*I +/ ( 0.00706834403694714484 + 0.0186497890361357298*I )
Examples
Several examples of pySecDec usage can be found in the source
code repository (examples
directory). Here are some of them:
easy
: a simple parametric integral, described in the manual in Section 2.1.box1L
: a simple 1loop, 4point, 4propagator integral, described in the manual Section 2.2.triangle2L
: a 2loop, 3point, 6propagator diagram, also containing massive propagators.box2L_numerator
: a massless planar onshell 2loop, 4point, 7propagator box with a numerator, either defined as an inverse propagatorbox2L_invprop.py
or in terms of contracted Lorentz vectorsbox2L_contracted_tensor.py
.triangle3L
: a 2loop, 3point, 7propagator integral, demonstrates that the symmetry finder can significantly reduce the number of sectors.elliptic2L_euclidean
: an integral known to contain elliptic functions, evaluated at a Euclidean phasespace point.elliptic2L_physical
: an integral known to contain elliptic functions, evaluated at a physical phasespace point.triangle2L_split
: a 2loop, 3point, 6propagator integral without a Euclidean region due to special kinematics.hypergeo5F4
: a general dimensionally regulated parameter integral, corresponding to a Hypergeometric function 5F4.4photon1L_amplitude
: calculation of the 4photon amplitude, showing how to use pySecDec as an integral library in a larger context.two_regulators
: an integral involving poles in two different regulators.userdefined_cpp
: a collection of examples demonstrating how to combine polynomials to be decomposed with other userdefined functions.
Development
During development instead of full installation it is more convenient to work directly from the checked out repository. To make this work, one needs to install the Python dependencies, build the contributed software, and setup PYTHONPATH to point to the sources; do this by running
$ make dependencies
$ make build
$ export PYTHONPATH=$PWD
The Makefile
in the package's root directory also implements
other common development tasks. You can list all available
targets with the command
$ make help
pySecDec
comes with a self test suite written in the python unittest
framework. The most convenient way to run all test is
using Nose. If Nose is installed (as it would be after make dependencies
), type
$ make check
in the source repository to run all tests. Developers should write test cases for ALL functions they implement and make sure that ALL tests pass before uploading a commit.
Building the Documentation
To build the documentation of pySecDec
, you need Sphinx. If
Sphinx is installed (as it would be after make dependencies
),
the command
$ make doc
generates the documentaion in html
and in pdf
format. Developers
should inlinedocument python functions and also keep the C++
part up to date. To generate HTML and PDF separately, use
$ make dochtml
and
$ make docpdf
Building the documentaion in pdf format requires an uptodate
installation of a latex implementation. If you get an error about
missing .sty
file, do the following:

If you are an administrator on your computer, try to install the missing latex packages with your favorite package manager. The TeXLive or MiKTeX implementations should contain all required packages.

If you are not an administrator, first get the missing packages, e.g. from CTAN. Collect the missing files in one or more directories and set the environment variable TEXINPUTS to these directories in the same way as the PATH variable is typically set.
Making a PyPI release
To create a release on PyPI, first increment the version number
of pySecDec in pyproject.toml
, and update CHANGELOG.md
. Then
make sure you have a recent Singularity installed, and run
./buildrelease.sh
This will create a source distribuion file (dist/*.tar.gz
)
and several prebuild distribution files (dist/*.whl
); it will
also print the instructions on how to doublecheck the files
with auditwheel and upload them to PyPI using Twine.
Note that an account with PyPI is needed for this. Please see the packaging python projects guide for details.
The reason for using Singularity here is because prebuilt distributions must be built inside one of the manylinux Docker images: this guarantees that the prebuilt libraries and programs will work on a wide range of Linux systems. If it wasn't for this requirement, then making a distibution would be as simple as running
$ make dist
and then uploading the distfiles in dist/
:
$ twine upload dist/pySecDec<version>.tar.gz
$ twine upload dist/pySecDec<version><tag>.whl
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